Self-attaching female fasteners, including pierce and clinch nuts, formed by cold header techniques and secondary press operations generally include a body portion having an end face, a central pilot portion projecting from the end face of the body portion having a bore through the central pilot portion, a flange portion surrounding the outer surface of the pilot portion including an annular groove surrounding the pilot portion and an annular planar panel support surface surrounding the annular groove. The bottom wall of the annular groove typically includes a plurality of circumferentially spaced convex or concave radial ribs which provide resistance to rotation of the nut or torque resistance following installation in a panel. In many applications, torque resistance is an important feature of the self-attaching nut. The outer surface of the flange portion is typically round or polygonal having six or more sides. U.S. Pat. Nos. 5,531,552, 5,549,430, 6,851,904, 6,994,500, 7,001,125, 7,112,024, 7,112,025 and 7,112,142 all assigned to the assignee of this application disclose this type of fastener. Other pierce and clinch nuts of this type are disclosed in U.S. Pat. Nos. 5,251,370, 6,220,804, U.S. Design Pat. Nos. D454,484 and D457,054 and European Patent No. EP 1 116 891 B1. U.S. Patent Publication No. US 2004/0234356 A1, assigned to the assignee of this application does disclose a self-attaching nut formed by cold header techniques which may be interconnected in side to side relation by frangible wires for continuous installation in a die press. However, the need remains for improved self-attaching nuts of this type including nuts which may be interconnected by frangible wires and self-attaching nuts having improved torque resistance.